Arriving back at LHR from ZRH will see you into T2. If hand luggage only, it should not be too bad. Of course, the number of arrivals in the same time slots as yourself will affect. I would guesstimate that from Doors Open at the gate, to the train platform should be 20/25 minutes, if moving smartly along and overtaking folks, once up the jetty into the concourse.
Your profile shows you in Essex so tough luck on not getting back to LCY. The fastest is the Heathrow Express into Paddington. It is expensive but they are paying and have stuffed you on the late arrival. From there, it's (probably) the dear old Circle as usual to Liverpool Street.
If you can arrange for anyone to meet you by car - that will speed up things considerably! Time might not permit but, at the start of the trip: Drive to LHR and park up in a mid-term park. Then use Train/Tube back to LCY. It will be a schlep but pay dividends on the return. Unless you want to drink on the way back!!